Radioactive disintegration isa first order reaction and it's rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure . The rate of radioactive disintegration (Activity) is represented as - (dN)/(dt) = lambda N , Where lambda = decay constant , N number of nuclei at time t, N_(0) = initial no. of nuclei. The above equation after integration can be represented as lambda = (2.303)/(t) "log" ((N_(0))/(N)) Half-life period of U^(232) is 2.5 xx 10^(5) years . In how much time will the amount of U^(237) remaining be only 25% of the original amount ?

Radioactive disintegration isa first order reaction and it's rate depe

1.	Radioactive disintegration isa first order reaction and it's rate depends only upon the nature of nucleus and does not depend upon external factors like temperature and pressure . The rate of radioactive disintegration (Activity) is represented as - (dN)/(dt) = lambda N , Where lambda = decay constant , N number of nuclei at time t, N_(0) = initial no. of nuclei. The above equation after integration can be represented as lambda = (2.303)/(t) "log" ((N_(0))/(N)) Half-life period of U^(232) is 2.5 xx 10^(5) years . In how much time will the amount of U^(237) remaining be only 25% of the original amount ?
Answer» `2. 5 xx 10^(5)` years `1.25 xx 10^(5)` years `5 xx 10^(5)` years `10^(6)` years SOLUTION :`t_(1//2) = 2.5 xx 10^(5)` years , `N_(0) OVERSET(t_(1//2)) (to) (N_0)/(2) overset(t_(1//2))(to) (N_(0))/(4) , t = 2 xx t_(1//2) = 5 xx 10^(5)`